Microphase separation of living cells

Self-organization of cells is central to a variety of biological systems and physical concepts of condensed matter have proven instrumental in deciphering some of their properties. Here we show that microphase separation, long studied in polymeric materials and other inert systems, has a natural counterpart in living cells. When placed below a millimetric film of liquid nutritive medium, a quasi two-dimensional, high-density population of Dictyostelium discoideum cells spontaneously assembles into compact domains. Their typical size of 100 μm is governed by a balance between competing interactions: an adhesion acting as a short-range attraction and promoting aggregation, and an effective long-range repulsion stemming from aerotaxis in near anoxic condition. Experimental data, a simple model and cell-based simulations all support this scenario. Our findings establish a generic mechanism for self-organization of living cells and highlight oxygen regulation as an emergent organizing principle for biological matter.


A. STEADY STATE
To ascertain that our system has reached a steady state, we considered several quantities: the background phase cell density, the mean aggregate size and the distribution of aggregate size.
Supplementary figure 1A shows a semilog plot of the background cell density ρ b as a function of time for the same medium height h = 1.5 mm but starting from different initial cell densities ρ 0 . Among the three independent experiments, the red curve corresponds to the experiment displayed in Fig. 1a-c of the main text (ρ 0 = 7.5 10 4 cm −2 ). The doubling time in the exponential growth phase is similar for the three experiments, with a value 8 ± 1 h. The background cell density after aggregation (indicated by arrows) is constant at about 5 ± 1 10 5 cm −2 .
The size of aggregate ( Supplementary Fig. 1B) also exhibits a plateau reached about 24 h to 36 h after the onset of aggregation. The red curve corresponds again to the experiment of Fig. 1a-c (h = 1.5 mm). The blue curve corresponds to the experiment of Fig. 1d-f of the main text (h = 0.85 mm, ρ 0 = 10 5 cm −2 ). For the latter, we show in Supplementary Fig. 1C two snapshots of the aggregates at times separated by 10 h. To the naked eye, there is no obvious change in the domain size. This can be confirmed quantitatively by computing the distributions of size and inter-aggregate distance ( Supplementary Fig. 1D-E). In both cases, there is no change in the histogram bin where the maximum is reached and the increase of the mean average size is only 5% after 10 h. To a very good approximation, one can consider the aggregate have indeed reached a steady state.
Finally, we also report in Supplementary Fig. 1B two experiments where the liquid film is topped with a thin layer of oil to reduce evaporation but not oxygen availability. The curve plateaus are also consistent with a steady state.
Remarkably, aggregates themselves remains very mobile and never settle into a static configuration. This is illustrated in Supplementary Movie 4 and in Supplementary Fig. 2, which shows the trajectory of many aggregates over one day. Aggregates actually move over a distance much larger than the typical inter-aggregate distance, and do so without coalescing or merging with their neighbours. The medium height is h = 1.5 mm and the init ial cell densitiesare ρ0 = 1.2 10 4 , 2.2 10 4 and 7.5 10 4 cm −2 for pink, black and red curves respectively. (B) Time evolution of the mean aggregate size a. Blue and red curves: the medium height is h = 0.85 and 1.5 mm respectively. Gray and black curves: two independent experiments where the liquid film is covered with 1.6 ml of paraffin to reduce evaporation, the medium height is h = 1.5 mm. (C) Snapshots of the experiment corresponding to the blue curve in (B) after t = 53 h and 10 h later. (D-E) Superimposed distributions of the domain size P (a ) and first neighbor's distance P (d ) for the two snapshots at t = 53 h (blue) and 10 h later (gray).

Aggregate cohesion
Dd cells in development stage in starvation buffers are known to possess three adhesive systems [1]. The first to be expressed is calcium dependent and can be disabled by EDTA (Ethylenediaminetetraacetic acid), a chelator of divalent ions.
Once aggregates reached their steady state, we added 20 µL EDTA at 500 µM in one well of a 6-well plate with about 2 mL of medium. The injection was made drop by drop as gently as possible to avoid any disturbance. The aggregates then start dissociating (Supplementary Movie 3), a process seen immediately in the injection zone and elsewhere in the subsequent hours. These observations indicate that the calcium dependent adhesive system is operative in a nutrient buffer at high cell density and that cell-cell adhesion is responsible for the aggregate cohesion.

Aggregate height
We first examine a typical aggregate, whose radius 70 µm is close to the typical value a = 65 ± 25 µm obtained with medium height h = 1.5 mm. To visualize the three-dimensional structure, we used Z-stacks in transmission mode using 10X objective lens on a confocal (Leica SP5, Germany). The reference slice at z = 0.00 µm ( Supplementary  Fig. 3A) shows the bottom of the aggregate surrounded by a first layer of cells spread on the substrate (yellow arrows) and not very mobile (Supplementary Movie 2). At z = 7.11 µm above the reference ( Supplementary Fig. 3B), a second layer of cells, more rounded and very mobile is present (red arrows). At z = 30.81 µm ( Supplementary Fig. 3C), we detect the aggregate upper boundary. Taking into account the uncertainty in the manual estimation of reference level (±2 µm) and of the upper boundary (±7 µm), this suggests a height around 30 ± 7 µm.
A second indication of aggregate height is provided by aggregates climbing PDMS vertical pillars, as illustrated in Supplementary Fig. 3D. Most aggregates had a height within 30 µm but aggregates as thick as 40 µm were occasionally encountered.

Aggregate cell density
To estimate the projected cell density in aggregates ρ a , we use the relationρ = φρ a + (1 − φ)ρ b . We consider the typical system shown in Fig. 1a-c and Fig. 2d with h = 1.5 mm of medium. From the measured mean cell densityρ = 0.8 10 6 cm −2 the background cell density ρ b = 0.5 10 6 cm −2 and the surface fraction φ = 0.2, one finds ρ a 2 10 6 cm −2 . Because of large error bars, the actual value may actually fall in large range around this average, but this provides at least a reasonable estimate.

C. AGGREGATE RESPONSE TO A STEP CHANGE IN OXYGEN
We show in Supplementary Fig. 4 the effect of increasing the amount of oxygen available to cells. Images are separated by 5 hours, a time interval during which cell division is negligible (see Note below). Whatever the initial state fixed by the medium height h -large or small aggregates -, the typical size of domains substantially increases.
key feature of microphase separation.
We illustrate in Supplementary Fig. 5 the effect of returning to normal oxygen level, after a temporary increase of 3.5 h during which, as above, cell division can be neglected. Though the characteristic radius of aggregates has roughly doubled at high oxygen level, aggregates recover their smaller initial size when going back to normal atmosphere. Such a decrease in size is a strong clue that aggregates are not governed by coarsening. Thus, whether being made artificially smaller as in Fig. 2e or larger as in Supplementary Fig. 5, aggregates return to a preferred domain size, which is a

Oxygen measurements
Oxygen concentration were obtained using a commercial optical "robust oxygen probe" (OXROB3) coupled to its oxymeter (Firesting, Pyroscience, Aachen, Germany). The measurement is based on the luminescence quenching by oxygen of a redflash indicator deposited at the probe tip.
We systematically controlled the oxygen content in our homemade environmental chamber. More specifically, we measured the gaseous volume percentage, defined as p O2 /p atm × 100%, where p O2 and p atm are respectively the partial pressure of oxygen and the barometric pressure of ambient air.
To obtain the oxygen concentration at saturation in the HL5 Dd growth medium under normal atmosphere, the probe was plunged in 6-mL bottle filled with the medium but no cells. At temperature 22°C , we found c s = 250±20 µM, in agreement with literature values [2].

Consumption of individual cells
To measure the oxygen consumption of cells, we filled a 6-mL glass bottle with a concentrated cell suspension, which contains typically 2 10 7 cells, and closed it with a cap through which the oxygen probe was plunged in the liquid. The cap was carefully sealed around the probe to avoid external oxygen entering the bottle. During the time required to prepared the cell suspension and the oxygen probe, the oxygen concentration inside the bottle dropped to about 200 µM. Then it linearly decreased to nearly zero in about 1600 s, as shown in Supplementary Fig. 6A. The cell oxygen consumption which is proportional to the slope of this curve is nearly constant (Supplementary Fig. 6B), with a value of q = 4.2 ± 0.8 10 −17 mol s −1 cell −1 (average over six experiments), in a concentration range extending from 150 µM down to a few µMs. For lower concentration, the consumption drops abruptly. The typical concentration at which cell consumption becomes concentration dependent is thus in the range 2.5 − 10 µM, which corresponds to c csm /c s in the range [0.01, 0.04].

Cell division at low oxygen concentration
Starting from very low cell densities at about 3000 cm −2 , we monitored the cell growth by timelapse microscopy under various atmosphere oxygen levels in our environmental chamber. Given the low cell densities which make total consumption small, the dissolved oxygen concentration in the culture medium is simply fixed by the oxygen level outside. Supplementary figure 7A shows a typical growth at two very different oxygen levels. In the initial atmospheric reference condition (21% O 2 , c = c s = 250 µM), the growth is exponential with division time T div 8 h (i.e. 4-fold increase during 16 h), in agreement with previous measurements [3] From 22 h to 45 h, pure N 2 was injected in our chamber up, leading to a residual level of 0.15% O 2 (c = 1.8 µM). During the first 6 hours of this severe hypoxic condition, the population continues to grow although at a decreasing rate. The cell number then reaches a plateau and eventually slightly decreases (the reason is that because some cells detach and round up, their optical contrast changes and they are partially undetected by the FindMaxima tool of ImageJ). Upon re-injection of 21% O 2 air at time 45 h, the population still slightly decreases during about 6 h, but it later recovers and grows again. These observations indicate that at c = 1.8 µM, cells finish their life cycle before entering a resting phase (quiescence). The existence of the 6 hours lag period upon air re-injection implies that after quiescence, cells need time to resume their normal life cycle.
We tested a range of oxygen levels and observed that the growth index, that is the fold change in the number of cells between between t = 0 h and t = 16 h, is changing with oxygen concentration (Supplementary Fig. 7B). In particular, at c = 5 µM and c = 12.5 µM, the growth index is N (16 h)/N (0 h) = 1.2 and 2 respectively. Our values (squares) are in agreement with literature values [4,5] for the AX3 cell lines (triangles and circles respectively). Interpolating the data with a simple exponential form (dotted line) leads to the estimate c div 10 µM for the concentration at which the growth is divided by two with respect to the reference in normoxic conditions. Accordingly, we use c div /c s = 0.05 in Equation (1) of the main text.

Model definition
Our simplified model for aggregate is shown in Supplementary Fig. 8. An aggregate is represented as a disk of zero thickness and radius a placed on the bottom surface. The cell density is ρ a within the aggregate and ρ b in the background outside. Because the mean cell densityρ will be fixed in the following, an aggregate can grow in size only by depleting the surrounding region. The individual cell consumption q is assumed constant. The oxygen flux consumed by the cells is J a = qρ a and J b = qρ b on the aggregate and background respectively. The aggregate is not isolated but surrounded by identical neighbours arranged on a hexagonal array. To make the calculation analytically tractable, the hexagonal boundary of the unit cell is replaced by a disk of radius b of equal area, so that azimuthal invariance is recovered. A vanishing lateral flux is imposed at this effective boundary. The concentration on the top surface is fixed to the saturation value c s . The surface fraction of aggregate is φ = a 2 /b 2 and the mean densitȳ ρ = φρ a + (1 − φ)ρ b . We will assume that the aggregate cell density ρ a is a fixed value, independent of aggregate size and surface fraction.

Derivation of analytical solution
Here we give the details of the derivation for the oxygen concentration field c(r, z), which is a purely diffusive problem. The notations are shown in Supplementary Fig. 8 Unless otherwise mentioned, we chose units so that h, D and c s are all unity. The equation and boundary conditions to be satisfied by f (r, z) are where ∆ = r −1 ∂ r (r∂ r ) + ∂ 2 zz denotes the Laplacian. The flux perpendicular to the lateral wall is taken as zero and J (r) is the arbitrary flux imposed on the bottom surface. Applying classical methods [6], the solution is Here, J n is the Bessel function of order n, µ m is the m th zero of J 0 = −J 1 , with the convention µ 1 = 0. We consider an imposed flux with H the Heaviside function, J ab ≡ J a − J b andJ = φJ a + (1 − φ)J b is the mean flux. We then find for the value at the bottom surface Now, putting back dimensions, the condition that the minimal concentration, obtained at r = 0 and z = 0, is the target valueĉ can be rewritten as where we used J ab = (J a −J)/(1 − (a/b) 2 ). Since fluxes are proportional to cell densities, Equation (6) gives back Eq. (2), where √ φ = a/b is assumed fixed. The function ψ(ζ, λ), computed numerically, is plotted in Supplementary Fig. 9. For λ = h/b > 1, the dependence on λ is negligible and ψ(ζ, λ) can be approximated as ψ(ζ, ∞). Taking ζ in the range [0.1, 1] includes all surface fraction of interest since φ = ζ 2 . In this domain, the function ψ(ζ, ∞) has limited variation, being confined in the interval [0.38 − 0.94] and remains a prefactor of order one. Note that this conclusion holds in most of the relevant parameter space but not in the vicinity of h min . In this region, the domain size a diverges while ψ(ζ, λ = √ φ h/a) approaches zero as λ → 0.

Choice of parameters
Here we explain the parameters taken in applying the model. The values for c s , D and q were introduced in the main text. The saturation concentration c s = 250 µM and the cell consumption rate q = 4.2 10 −17 mol s −1 , were both measured experimentally as detailed in Section D of Supplementary Information, The diffusion coefficient is D = 2 10 −5 cm 2 s −1 . For the aggregate (projected) cell density, a reasonable estimate is ρ a = 2 10 6 cm −2 (Section B of Supplementary Information) which corresponds to h min = 0.55 mm according to Eq. (3). As regards the critical concentrationĉ, the steady state we consider has constant cell number because cells have stopped dividing (Supplementary Fig. 1A), which suggests a concentration below c div everywhere, and a significantly lower value at the aggregate center where it is minimal. We therefore fixĉ/c s = 0.01 and note that this value could be doubled or halved with comparable results. Finally, the surface fraction φ remains a free parameter. It is bounded by the maximal value φ max =ρ/ρ a reached when all cells are inside aggregates and none outside (empty background with ρ b = 0). It turns out that the choice of φ between φ max and lower values (0.16 φ max for instance in Fig. 3e) has only a limited influence on the results, as visible in Fig. 3e.  For each point of Fig. 1e, identified by color and film thickness h, we report in Supplementary Table 1 the mean number of aggregates by frame (N agg,frame ) as well as the number of frames used to obtain the point (N frame ).